This is a slightly modified copy/paste from an identical post of mine on the Mage forums, so please bear with any formatting errors and the rather dumbed-down initial explanation. I was directed here for help in improving and expanding upon the post and it's calculations, and possibly locating some useful spreadsheets and such. Any such help would be appreciated. There didn't seem to be a fresh topic that I could post this under without derailing, so I made a new one.

Off of the Mage Forums:

Okay, this is a comparison of Scorch to Frostbolt in terms of effective damage scaling, and I hope to be able to eventually include every variable into it, I have figured out every variable except Combustion and Ignite rolling and would like help with these if anyone can. Lots of math, please, PLEASE, correct me if I am wrong on any of it. If you want, you can biohazard this for a sticky once it's fleshed out.

The summarizations of the formula and titles of formula walkthroughs will be bolded, if you want to identify what each portion of the formula represents you can check the walkthrough above the summarization to determine that. This is comparing two builds, that include all the damage talents possible for Scorch and Frostbolt. This requires 30 points in Frost and 31 points in Fire. The extra point in Frost could potentially be spent in a damage talent such as PoM, but that will be ignored since it does not directly affect either Frostbolt or Scorch. Note that "leech" specs such as 23/0/28 will not be calculated.

Now, what is damage efficiency and why is it important, exactly? Damage efficiency is, essentially, how well a spell scales with gear. For example, Cone of Cold has terrible damage efficiency, even when talented. Frostbolt however, has many talents to improve it's damage efficiency, and gets a large % of +damage to boot, so it's efficiency is excellent in comparison.

But why is it important? I'll give an example: Firepower gives 10% extra damage on your scorch. What this means is, your Scorches gain three qualities: They now do 10% more DPS, cost 10% less DPM, and best of all scale 10% better with damage gear! Firepower is an amazing talent, simply put. However, there have already been tons of calculations done to determine DPS and DPM simply and easily, so I went ahead and did efficiency instead.

Now, to get started:

First of all, we're gonna be using a timeframe for this scaling of 3.0

This is the base scaling for a Frostbolt cast as well as the cast time for two scorches.

Now, the base multiplier is 1.00 or 100% damage scaling.

Base untalented frostbolt = 1.00
Base untalented scorch = 1.00

Frostbolt:

Multipliers: 3.0 second casting time, snare penalty, Improved Frostbolt, Ice Shards, Piercing Ice, Winter's Chill, 2.0 Crit damage.

Initially, frostbolt has a cast time of 3.0 seconds. This means it gets a multiplier of 1.0 * (3.0 / 3.5), or, .857 for it's 3.0 second casting time.

Frostbolt also has a damage scaling penalty of .05 due to the snare. This means you end up with .857 * .95 = .81415 for the snare penalty.

The first talented multipiler to include is Improved Frostbolt. For this calculation you get 3.0 seconds worth of casting time in 2.5 seconds. So, the starting formula is .81415 = 2.5 , (Improved Frostbolt) = 3.0

So, to figure this out you simply: 3.0 / 2.5 * .81415 = .97698 so with Improved Frostbolt the scaling comes up to .97698

Next, Piercing Ice: .97698 * 1.06 = 1.0355988

Fully talented, Frostbolt has a base damage efficiency of 1.0355988 neither rounded up or down whatsoever as you can tell.

Now, from here the variables have to be personally tailored by you, variables such as crit and latency, and eventually +dmg.

The first formula for you to plug a number in is crit.

For Frost, one percent of crit directly equates to a 1% increase in dps. You have a talent named Winter's Chill that gives +10 to base crit. So, the calculation is simple:

1.0355988 * (crit percentage + 1.1) = damage efficiency with crit included.

I'll use my crit as an example, this is likely not going to be the same as yours but for those looking for a rough estimate it shouldn't be too far off track: 13.76%

1.0355988 * (.1376 + 1.1) = 1.28166(rounded) , that is my personal damage efficiency including crit. This is rounded to the fourth decimal place for simplicity.

The next calculation to do here is latency, another stat that only you can provide. This calculation, for Frostbolt, modifies your Frostbolt by making it's 2.5 second cast time into (2.5 seconds + latency).

The formula is going to be: 2.5 / (2.5 + latency) * 1.0355988 * [crit percentage]).

Now, this needs an example, so we will use my crit and latency:

2.5 / (2.5 + 0.2) = .9259(rounded)
* 1.28166 = 1.186688994

So, for me, my Frostbolt damage efficiency with crits and latency included is 1.186688994

Summarization of formula:

1.00 x (3.0 / 3.5) * .95 = .81415

3.0 / 2.5 * .81415 * 1.06 = 1.0355988

1.0355988 * (crit percentage + 1.1) = x

2.5 / (2.5 + latency) * x = y

y = damage efficiency for Frostbolt.

I do not currently have a modifier for if you have +8/8 NW, if someone can provide a clear cut formula for the efficiency increase this adds I will try to add it in, but if you consider things such as latency this may prove to be difficult or impossible.

Scorch:

Multipliers: Ignite, Incinerate, Improved Scorch, Firepower, Critical Mass, Combustion.

Scorch's base multiplier is 1.00, untalented before crits, , +dmg gear, or latency of any sort.

Scorch has a .43 damage efficiency scale from it's 1.5 second casting time. In a 3 second period, we can cast two scorches without lag, so the scale becomes .86

The first multiplier to calculate is Improved Scorch, so: * 1.15 = .989

Fire Power: .989 * 1.10 = 1.0879

Critical strikes with Scorch do 210% damage, so each percent of crit for fire can be said to equal 1.1% DPS.

Additionally, you have Incinerate and Critical Mass, which add 10% to your base crit.

Not only is initial Scorch crit damage affected by Improved Scorch and other debuffs, but the Ignite ticks are as well, for another stacking multiplier.

Therefore, to calculate crit the formula is: 1.0879 * ([crit + .1] * .5) + [(crit + .1) * .6 * 1.15) = damage efficiency with crit included, factoring in ignite's ticks gaining additional benefit from Improved Scorch.

As an example we will use my base crit of 13.76%:
1.0879 * ([.1376 + .1] * .5) = 1.217(rounded)
1.217 + [(.1376 + .1) * .6 * 1.15] = 1.380944(rounded)

After Incinerate, Critical Mass, and Ignite, my Scorch has a damage efficiciency of 1.380944

Now, for latency: This modifier changes your two Scorches per three seconds by making their 3 second cast time into

(3.0 + [latency * 2]).

So, the formula is: 3.0 / (3.0 + [latency * 2]) *1.0879 * ([crit + .1] * .5) + [(crit + .1) * .6 * 1.15) = damage efficiency with latency included.

As an example: 3.0 / 3.4 = .8823(rounded)
.8823 * 1.380944 = 1.2184(rounded)

So, with latency and crits included, my damage efficiency with Scorch is 1.2483

Summarization of formula:

.86 * 1.15 * 1.10 = 1.0879

1.0879 * ([crit + .1] * .5) + [(crit + .1) * .6 * 1.15) = x

3.0 / (3.0 + [latency * 2]) * x = y

y = damage efficiency with Scorch


The scorch numbers do NOT include rolling ignites and Combustion, because determining those would require huge and complex matrixes which I am not capable of creating. If anyone can link a working spreadsheet or something I will plug it into my post so readers can just put their numbers into the spreadsheet and come out with a more appropriate efficiency.

Wishlist:

Matrix for NW Focus
Matrix for Combustion
Matrix for rolling ignites


Please read, and REPLY!

I look forward to Ice Lance.

I think I found a small logic flaw in your calculation of scorch crit increase.

When you add the crit bonus, you're adding in improved scorch incorrectly I believe. I don't play a mage, but to my knowledge, it's only the ignite ticks themselves that get the 2nd bonus from the improved scorch debuff. What you're doing, as near as I can tell, is calculating the entire crit with an additional improved scorch, when in reality the initial 50% damage bonus on the crit does not recieve an extra imp scorch modifier.


You know what you might have to do? split your crit modification calculations apart. One, the initial damage boost at 150% of your normal hit, then in a separate second step calculate your ignite damage. This might also let you estimate rolling ignites easier.

This is correct.

Fire effectively crits at 219% with Imp. Scorch up. (Or, 252% of what your base Fire non-crit would have done without Imp. Scorch).

Amusingly enough, against Thaddius, a Fire crit does 350% of a non-crit, or 1168% of the tooltip non-crit damage.

Checking math,
Scorch does 100, with firepower it will do [100*1.10]=110, with debuff it will do [110*1.15]=126.5
On a crit, [126.5*1.50]=189.75 and ignite for [189.75*0.40*1.15]=87.285
So a 110 firepower scorch does [189.75+87.285]

[top]277.035

227.035/126.5

219% on crits.

Bah, Arawethion beat me as I was typing something else that made no sense even to me and thusly deleted it.

Wait, I totally forgot about Fire Power. Does that pull double duty as well?

I see the problem and will correct it in the next few hours. I don't fully understand the methods you two are using though, so I'll just modify my existing stuff and if you want you can check it against your methods and see if it comes out to be similar.

What don't you get? Feel free to ask a question, I can always explain what I did a bit more.

I have very odd ways of doing calculations like these, mostly in my head, and I just didn't understand the way you were doing them in. It doesn't click for me. It's updated now so you can just check over it and compare results if you want.

Fire Power does not double the buff on ignite. I have yet to check Power Infusion.